[R-meta] phylogenetic information in both moderator and random part of rma.mv?

[Viechtbauer, Wolfgang (NP)]

1|id is an 'observation-level random effect'. This is one of the core elements of a meta-analysis to model heterogeneity (i.e., variance) in the underlying true outcomes. In a standard linear regression-type model (or mixed-effects model), it is not possible to add such a random effect, because it is completely confounded with the error term (the error term in a standard regression model *is* an observation-level random effect). However, in meta-analytic models, it is possible to add such a random effect, because the model does not contain a separate error term -- the sampling variances of the errors are fed into the model as known constants.

Best,
Wolfgang

>-----Original Message-----
>From: Sigurd Einum [mailto:sigurd.einum using ntnu.no]
>Sent: Friday, 30 September, 2022 13:06
>To: Viechtbauer, Wolfgang (NP); r-sig-meta-analysis using r-project.org
>Subject: RE: phylogenetic information in both moderator and random part of
>rma.mv?
>
>There are (usually) several rows (observations of Y and associated sampling
>variance) for each species, as well as for each study. Hence the random structure
>~ 1|study, ~ 1|species.
>
>I tried adding the id variable and the 1|id random structure as you recommended
>(model estimates of class parameters remain basically unaltered, whereas AICc
>drops a lot), but I don't really understand what this achieves, and I have never
>used or encountered the use of such a structure with each observed data point
>being assigned a separate random effect in mixed models (lme/lmer) previously. Is
>it somehow related to the weight= varIdent in lme, which allows for different
>random effects for different groups of observations? But in this case the model
>allows for different random effects for each single observation? It is probably
>beyond me to understand this (I'm not a statistician), which is fine, but if
>possible I would like to try, so if you can point me to a resource where I could
>read up on this that would be great. I read through this
>https://wviechtb.github.io/metafor/reference/rma.mv.html but still not sure I got
>it.
>
>Thanks again for all your helpful advice!
>Sigurd
>
>>-----Original Message-----
>>From: Viechtbauer, Wolfgang (NP)
>><wolfgang.viechtbauer using maastrichtuniversity.nl>
>>Sent: Friday, September 30, 2022 11:45 AM
>>To: r-sig-meta-analysis using r-project.org
>>Cc: Sigurd Einum <sigurd.einum using ntnu.no>
>>Subject: RE: phylogenetic information in both moderator and random part of
>>rma.mv?
>>
>>Sounds reasonable.
>>
>>One additional thing: I don't know what your data structure actually looks like.
>Is
>>each row a different study? Or is each row a different species? If not, then I
>>would strongly suggest to include '~ 1 | id' where
>>
>>Final.data$id <- 1:nrow(Final.data)
>>
>>as a random effect (in both mod1 and mod2). Otherwise you would be assuming
>>homogeneity of true outcomes within studies/species, which is a strong
>>assumption.
>>
>>Best,
>>Wolfgang